Simplification and solving of equation

1. The problem statement, all variables and given/known data
The problem are two:
(1) Simplify: 1/4(2[sup]n[sup/]- 2[sup]n+2[sup/])

(2) Solve the equation 2[sup](2x+1)- 9(2[sup]x[sup/] + 4 = 0
2. Relevant equations

3. The attempt at a solution
for the number one question, simplify:
1/4(2[sup]n[sup/]- 2[sup]n+2[sup/])

1/4(2[sup]n[sup/]- 2[sup]n+2[sup/])
= 4[sup]-1[sup/](2[sup]n[sup/]-2[sup]n+2[sup/])
= 2[sup](-2)[sup/](2[sup]n[sup/]-2[sup]n+2[sup/])
= 2[sup](-2)[sup/](2[sup]n[sup/]-2[sup]n[sup/]*2[sup]2[sup/]
I can't go further please I need asistance.

For the second question, solve the equation:
2[sup](2x+1)- 9(2[sup]x[sup/] + 4 = 0
I don't just know how to start dealing with the question. It is really a troubsome question.

Use [S U P] and [/S U P] (but with no spaces), not [sup ] and [ /sup]. In fact, just use the "X²" button on the palette at the top in the input panel.

RGV

I'm confused as to your original equations.

$$(1)\frac{1}{4}2^n-2^{n+2}$$
$$(2)\ 2^{2x+1} - 9(2^x + 4)$$

Are those correct?

For (1), you are close. Combine like terms.

For (2), it is actually a quadratic. Can you see what the variable is?

If like terms is collected, the expression will look like this:
2^(-2)*2²(2ⁿ-2ⁿ)

= 2^(-2)(2ⁿ-2ⁿ⁺²)
= 2^(-2)(2ⁿ-2ⁿ*2²

No! I didn't see the variable.

If like terms is collected, the expression will look like this:
2^(-2)*2²(2ⁿ-2ⁿ)
= 2(2ⁿ-2ⁿ)
= 2ⁿ⁺¹-2ⁿ

1/4(2ⁿ- 2ⁿ⁺²)

1/4(2ⁿ- 2ⁿ⁺²)
= 4^-1(2ⁿ-2ⁿ⁺²)
= 2^(-2)(2ⁿ-2ⁿ⁺²)
= 2^(-2)(2ⁿ-2ⁿ*2²)

No! I didn't see the variable.

I don't understand what you guys are writing, write using the same format I used in showing my raise to power in my opening post. I will understand it better and therefore be able to respond to the numerous replies you guys are posting.

You can't see Latex? I think you should try find out and fix what the problem is on your end, because Latex is commonly used on this forum and not just in this thread.

Please help me, I belive I would be able to understand and write using latex with time. Please help me, I really need this help please!

This does not follow from the last line you had written in your opening post:


What we have so far is

2^-2*(2ⁿ - 2ⁿ*2²)

Can you expand this?


There is a basic rule of exponentiation that says that if you exponentiate an exponent, you multiply the exponents together. What this is saying is that
(a^m)ⁿ=a^mn

So then what does (2^x)² simplify to?

Nope. Look at the last step in your original post:

Answer this: what is x - 4x?
Now answer this: what is 2ⁿ - 4*2ⁿ?
That's what Villyer meant by combining terms.


2^2x+1 - 9*2^x + 4
Rewrite the 1st term so it looks like (something) times 2^2x.


EDIT: Beaten to it.

Please help me, I belive I would be able to understand and write using latex with time. Please help me, I really need this help please!

You have been given lots of help---any more help and we would be doing your homework for you. If you are having trouble understanding what people write you need to sit down with a pencil and several sheets of paper and start writing things down in whatever notation you like.

RGV

I did not ask you to do my home work. What I ask is this: give me directions that will help me do the homework. That's all that I ask, anything far from that then you are doing my homework. I know that you are giving me some asistance, but how can I work with the language I don't understand. I know that apart from latex, there are other formats that can be used and I will be able to understand all the replies you are posting and be able to respond accordingly.

Here is what one responder said to you:

"Answer this: what is x - 4x?

Now answer this: what is 2ⁿ - 4*2ⁿ? "

So, what are your answers? Do you see why the answers are important?

RGV